For an $\omega $-categorical theory T and model $\mathcal {M}$ of T we define a hierarchy of ranks, the n-ranks for $n < \omega $ which only care about imaginary elements “up to level n,” where level n contains every element of M and every imaginary element that is an equivalence class of an $\emptyset $-definable equivalence relation on n-tuples of elements from M. Using the n-rank we define the notion of n-independence. For all $n < \omega $, the n-independence relation restricted to $M_n$ has all properties of an independence relation according to Kim and Pillay [17] with the possible exception of the symmetry property. We prove that, given any $n < \omega $, if $\mathcal {M} \models T$ and the algebraic closure in $\mathcal {M}^{\text {eq}}$ restricted to imaginary elements “up to level n” which have n-rank 1 (over some set of parameters) satisfies the exchange property, then n-independence is symmetric and hence an independence relation when restricted to $M_n$. Then we show that if n-independence is symmetric for all $n < \omega $, then T is rosy. An application of this is that if T has geometric elimination of imaginaries and the algebraic closure in $\mathcal {M}$ restricted to elements of M of 0-rank 1 (over some set of parameters from $M^{\text {eq}}$) satisfies the exchange property, then T is superrosy with finite $U^{{{\unicode{x00FE}} }}$-rank.